Extended harmonic analysis of phase space representations for the Galilei group (Q1082462)

A systematic method for finding all the irreducible subrepresentations of the projective phase space representations [the second author, Stochastic quantum mechanics and quantum spacetime (1984; Zbl 0536.60100)] of the Galilei group is presented. The spaces of the irreducible subrepresentations are shown to be reproducing kernel Hilbert spaces and a physical interpretation of the obtained results is then given in terms of systems of covariance [cf. the authors, Acta Appl. Math. 6, 1-18 (1986; see the preceding review)].